#### Document Type

Conference Proceeding

#### Language

eng

#### Format of Original

5 p.

#### Publication Date

11-1983

#### Publisher

American Mathematical Society

#### Source Publication

Proceedings of the American Mathematical Society

#### Source ISSN

0002-9939

#### Original Item ID

doi: 10.1090/S0002-9939-1983-0715874-4; Shelves: QA1 .A5215 Storage S

#### Abstract

We answer some questions raised in [1]. In particular, we prove: (i) Let *F* be a compact subset of the euclidean plane *E ^{2}* such that no component of

*F*separates

*E*

^{2}. Then

*E*can be partitioned into simple closed curves iff F is nonempty and connected. (ii) Let

^{2}\F*F Ç E*

^{2}be any subset which is not dense in

*E*, and let

^{2}*S*be a partition of

*E*into simple closed curves. Then

^{2}\F*S*has the cardinality of the continuum. We also discuss an application of (i) above to the existence of flows in the plane.

## Comments

Published version.

Proceedings of the American Mathematical Society, Vol. 89, No. 3 (November 1983): 498-502. DOI. © American Mathematical Society 1983. Used with permission.